My friend Xan found the following chart by Pew hard to understand. Why is the chart so taxing to look at?

It's packing too much.

I first notice the shaded areas. Shading usually signifies "look here". On this chart, the shading is highlighting the least important part of the data. Since the top line shows applicants and the bottom line admitted students, the shaded gap displays the rejections.

The numbers printed on the chart are growth rates but they confusingly do not sync with the slopes of the lines because the vertical axis plots absolute numbers, not rates.

The vertical axis presents the total number of applicants, and the total number of admitted students, in each "bucket" of colleges, grouped by their admission rate in 2017. On the right, I drew in two lines, both growth rates of 100%, from 500K to 1 million, and from 1 to 2 million. The slopes are not the same even though the rates of growth are.

Therefore, the growth rates printed on the chart must be read as extraneous data unrelated to other parts of the chart. Attempts to connect those rates to the slopes of the corresponding lines are frustrated.

Another lurking factor is the unequal sizes of the buckets of colleges. There are fewer than 10 colleges in the most selective bucket, and over 300 colleges in the largest bucket. We are unable to interpret properly the total number of applicants (or admissions). The quantity of applications in a bucket depends not just on the popularity of the colleges but also the number of colleges in each bucket.

The solution isn't to resize the buckets but to select a more appropriate metric: the number of applicants per enrolled student. The most selective colleges are attracting about 20 applicants per enrolled student while the least selective colleges (those that accept almost everyone) are getting 4 applicants per enrolled student, in 2017.

As the following chart shows, the number of applicants has doubled across the board in 15 years. This raises an intriguing question: why would a college that accepts pretty much all applicants need more applicants than enrolled students?

Depending on whether you are a school administrator or a student, a virtuous (or vicious) cycle has been realized. For the top four most selective groups of colleges, they have been able to progressively attract more applicants. Since class size did not expand appreciably, more applicants result in ever-lower admit rate. Lower admit rate reduces the chance of getting admitted, which causes prospective students to apply to even more colleges, which further suppresses admit rate.

National Geographic features this graphic illustrating migration into the U.S. from the 1850s to the present.

What to Like

It's definitely eye-catching, and some readers will be enticed to spend time figuring out how to read this chart.

The inset reveals that the chart is made up of little colored strips that mix together. This produces a pleasing effect of gradual color gradation.

The white rings that separate decades are crucial. Without those rings, the chart becomes one long run-on sentence.

Once the reader invests time in learning how to read the chart, the reader will grasp the big picture. One learns, for example, that migrants from the most recent decades have come primarily from Latin America (orange) or Asia (pink). Migrants from Europe (green) and Canada (blue) came in waves but have been muted in the last few decades.

What's baffling

Initially, the chart is disorienting. It's not obvious whether the compass directions mean anything. We can immediately understand that the further out we go, the larger numbers of migrants. But what about which direction?

The key appears in the legend - which should be moved from bottom right to top left as it's so important. Apparently, continent/country of origin is coded in the directions.

This region-to-color coding seems to be rough-edged by design. The color mixing discussed above provides a nice artistic effect. Here, the reader finds out that mixing is primarily between two neighboring colors, thus two regions placed side by side on the chart. Thus, because Europe (green) and Asia (pink) are on opposite sides of the rings, those two colors do not mix.

Another notable feature of the chart is the lack of any data other than the decade labels. We won't learn how many migrants arrived in any decade, or the extent of migration as it impacts population size.

A couple of other comments on the circular design.

The circles expand in size for sure as time moves from inside out. Thus, this design only works well for "monotonic" data, that is to say, migration always increases as time passes.

The appearance of the chart is only mildly affected by the underlying data. Swapping the regions of origin changes the appearance of this design drastically.

Alberto Cairo introduces another one of his collaborations with Google, visualizing Google search data. We previously looked at other projects here.

The latest project, designed by Schema, Axios, and Google News Initiative, tracks the trending of popular news stories over time and space, and it's a great example of making sense of a huge pile of data.

The design team produced a sequence of graphics to illustrate the data. The top news stories are grouped by category, such as Politics & Elections, Violence & War, and Environment & Science, each given a distinct color maintained throughout the project.

The first chart is an area chart that looks at individual stories, and tracks the volume over time.

To read this chart, you have to notice that the vertical axis measuring volume is a log scale, meaning that each tick mark up represents a 10-fold increase. Log scale is frequently used to draw far-away data closer to the middle, making it possible to see both ends of a wide distribution on the same chart. The log transformation introduces distortion deliberately. The smaller data look disproportionately large because of it.

The time scrolls automatically so that you feel a rise and fall of various news stories. It's a great way to experience the news cycle in the past year. The overlapping areas show competing news stories that shared the limelight at that point in time.

Just bear in mind that you have to mentally reverse the distortion introduced by the log scale.

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In the second part of the project, they tackle regional patterns. Now you see a map with proportional symbols. The top story in each locality is highlighted with the color of the topic. As time flows by, the sizes of the bubbles expand and contract.

Sometimes, the entire nation was consumed by the same story, e.g. certain obituaries. At other times, people in different regions focused on different topics.

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In the last part of the project, they describe general shapes of the popularity curves. Most stories have one peak although certain stories like U.S. government shutdown will have multiple peaks. There is also variation in terms of how fast a story rises to the peak and how quickly it fades away.

The most interesting aspect of the project can be learned from the footnote. The data are not direct hits to the Google News stories but searches on Google. For each story, one (or more) unique search terms are matched, and only those stories are counted. A "control" is established, which is an excellent idea. The control gives meaning to those counts. The control used here is the number of searches for the generic term "Google News." Presumably this is a relatively stable number that is a proxy for general search activity. Thus, the "volume" metric is really a relative measure against this control.

Yesterday, in the front page of the Business section, the New York Times published a pair of charts that perfectly captures the story of the ongoing turbulence in the stock market.

Here is the first chart:

Most market observers are very concerned about the S&P entering "correction" territory, which the industry arbitrarily defines as a drop of 10% or more from a peak. This corresponds to the shortest line on the above chart.

The chart promotes a longer-term reflection on the recent turbulence, using two reference points: the index has returned to the level even with that at the start of 2018, and about 16 percent higher since the beginning of 2017.

This is all done tastefully in a clear, understandable graphic.

Then, in a bit of a rhetorical flourish, the bottom of the page makes another point:

When viewed back to a 10-year period, this chart shows that the S&P has exploded by 300% since 2009.

A connection is made between the two charts via the color of the lines, plus the simple, effective annotation "Chart above".

The second chart adds even more context, through vertical bands indicating previous corrections (drops of at least 10%). These moments are connected to the first graphic via the beige color. The extra material conveys the message that the market has survived multiple corrections during this long bull period.

Together, the pair of charts addresses a pressing current issue, and presents a direct, insightful answer in a simple, effective visual design, so it hits the Trifecta!

***

There are a couple of interesting challenges related to connecting plots within a multiple-plot framework.

While the beige color connects the concept of "market correction" in the top and bottom charts, it can also be a source of confusion. The orientation and the visual interpretation of those bands differ. The first chart uses one horizontal band while the chart below shows multiple vertical bands. In the first chart, the horizontal band refers to a definition of correction while in the second chart, the vertical bands indicate experienced corrections.

Is there a solution in which the bands have the same orientation and same meaning?

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These graphs solve a visual problem concerning the visualization of growth over time. Growth rates are anchored to some starting time. A ten-percent reduction means nothing unless you are told ten-percent of what.

Using different starting times as reference points, one gets different values of growth rates. With highly variable series of data like stock prices, picking starting times even a day apart can lead to vastly different growth rates.

The designer here picked several obvious reference times, and superimposes multiple lines on the same plotting canvass. Instead of having four lines on one chart, we have three lines on one, and four lines on the other. This limits the number of messages per chart, which speeds up cognition.

The first chart depicts this visual challenge well. Look at the start of 2018. This second line appears as if you can just reset the start point to 0, and drag the remaining portion of the line down. The part of the top line (to the right of Jan 2018) looks just like the second line that starts at Jan 2018.

However, a closer look reveals that the shape may be the same but the magnitude isn't. There is a subtle re-scaling in addition to the re-set to zero.

The same thing happens at the starting moment of the third line. You can't just drag the portion of the first or second line down - there is also a needed re-scaling.

On the occasion of the hit movie Crazy Rich Asians, the New York Times did a very nice report on Asian immigration in the U.S.

The first two graphics will be of great interest to those who have attended my free dataviz seminar (coming to Lyon, France in October, by the way. Register here.), as it deals with a related issue.

The first chart shows an income gap widening between 1970 and 2016.

This uses a two-lines design in a small-multiples setting. The distance between the two lines is labeled the "income gap". The clear story here is that the income gap is widening over time across the board, but especially rapidly among Asians, and then followed by whites.

The second graphic is a bumps chart (slopegraph) that compares the endpoints of 1970 and 2016, but using an "income ratio" metric, that is to say, the ratio of the 90th-percentile income to the 10th-percentile income.

Asians are still a key story on this chart, as income inequality has ballooned from 6.1 to 10.7. That is where the similarity ends.

Notice how whites now appears at the bottom of the list while blacks shows up as the second "worse" in terms of income inequality. Even though the underlying data are the same, what can be seen in the Bumps chart is hidden in the two-lines design!

In short, the reason is that the scale of the two-lines design is such that the small numbers are squashed. The bottom 10 percent did see an increase in income over time but because those increases pale in comparison to the large incomes, they do not show up.

What else do not show up in the two-lines design? Notice that in 1970, the income ratio for blacks was 9.1, way above other racial groups.

Kudos to the NYT team to realize that the two-lines design provides an incomplete, potentially misleading picture.

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The third chart in the series is a marvellous scatter plot (with one small snafu, which I'd get t0).

What are all the things one can learn from this chart?

There is, as expected, a strong correlation between having college degrees and earning higher salaries.

The Asian immigrant population is diverse, from the perspectives of both education attainment and median household income.

The largest source countries are China, India and the Philippines, followed by Korea and Vietnam.

The Indian immigrants are on average professionals with college degrees and high salaries, and form an outlier group among the subgroups.

Through careful design decisions, those points are clearly conveyed.

Here's the snafu. The designer forgot to say which year is being depicted. I suspect it is 2016.

Dating the data is very important here because of the following excerpt from the article:

Asian immigrants make up a less monolithic group than they once did. In 1970, Asian immigrants came mostly from East Asia, but South Asian immigrants are fueling the growth that makes Asian-Americans the fastest-expanding group in the country.

This means that a key driver of the rapid increase in income inequality among Asian-Americans is the shift in composition of the ethnicities. More and more South Asian (most of whom are Indians) arrivals push up the education attainment and household income of the average Asian-American. Not only are Indians becoming more numerous, but they are also richer.

An alternative design is to show two bubbles per ethnicity (one for 1970, one for 2016). To reduce clutter, the smaller ethnicites can be aggregated into Other or South Asian Other. This chart may help explain the driver behind the jump in income inequality.

The Thai cave rescue was a great story with a happy ending. It's also one that lends itself to visualization. A good visualization can explain the rescue operation more efficiently than mere words.

A good visual should bring out the most salient features of the story, such as:

Why the operation was so daunting?

What were the tactics used to overcome those challenges?

How long did it take?

What were the specific local challenges that must be overcome?

Were there any surprises?

In terms of what made the rescue challenging, some of the following are pertinent:

How far in they were?

How deep were they trapped?

How much of the caves were flooded? Why couldn't they come out by themselves?

How much headroom was there in different sections of the cave "tunnel"?

There were many attempts at visualizing the Thai cave rescue operation. The best ones I saw were: BBC (here, here), The New York Times (here), South China Morning Post (here) and Straits Times (here). It turns out each of these efforts focuses on some of the aspects above, and you have to look at all of them to get the full picture.

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BBC's coverage began with a top-down view of the route of the rescue, which seems to be the most popular view adopted by news organizations. This is easily understood because of the standard map aesthetic.

The BBC map is missing a smaller map of Thailand to place this in a geographical context.

While this map provides basic information, it doesn't address many of the elements that make the Thai cave rescue story compelling. In particular, human beings are missing from this visualization. The focus is on the actions ("diving", "standing"). This perspective also does not address the water level, the key underlying environmental factor.

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Another popular perspective is the sideway cross-section. The Straits Times has one:

The excerpt of the infographic presents a nice collection of data that show the effort of the rescue. The sideway cross-sectional section shows the distance and the up-and-down nature of the journey, the level of flooding along the route, plus a bit about the headroom available at different points. Most of these diagrams bring out the "horizontal" distance but somehow ignore the "vertical" distance. One possibility is that the real trajectory is curvy - but if we can straighten out the horizontal, we should be able to straighten out the vertical too.

The NYT article gives a more detailed view of the same perspective, with annotations that describe key moments along the rescue route.

If, like me, you like to place humans into this picture, then you have to go back to the Straits Times, where they have an expanded version of the sideway cross-section.

This is probably my most favorite single visualization of the rescue operation.

There are better cartoons of the specific diving actions, though. For example, the BBC has this visual that shows the particularly narrow part of the route, corresponding to the circular inset in the Straits Times version above.

There is one perspective that curiously has been underserved in all of the visualizations - this is the first-person perspective. Imagine the rescuer (or the kids) navigating the rescue route. It's a cross-section from the front, not from the side.

Various publications try to address this by augmenting the top-down route view with sporadic cross-sectional diagrams. Recall the first map we showed from the BBC. On the right column are little annotations of this type (here):

I picked out this part of the map because it shows that the little human figure serves two potentially conflicting purposes. In the bottom diagram, the figurine shows that there is limited headroom in this part of the cave, plus the actual position of the figurine on the ledge conveys information about where the kids were. However, on the top cross-section, the location of the figure conveys no information; the only purpose of the human figure is to show how tall the cave is at that site.

The South China Morning Post (here - site appears to be down when I wrote this) has this wonderful animation of how the shape of the headroom changed as they navigated the route. Please visit their page to see the full animation. Here are two screenshots:

This little clip adds a lot to the story! It'd be even better if the horizontal timeline at the bottom is replaced by the top-down route map.

Someone sent me this via Twitter, found on the Data is Beautiful reddit:

The chart does not deliver on its promise: It's tough to know which birds like which seeds.

The original chart was also provided in the reddit:

I can see why someone would want to remake this visualization.

Let's just apply some Tufte fixes to it, and see what happens.

Our starting point is this:

First, consider the colors. Think for a second: order the colors of the cells by which ones stand out most. For me, the order is white > yellow > red > green.

That is a problem because for this data, you'd like green > yellow > red > white. (By the way, it's not explained what white means. I'm assuming it means the least preferred, so not preferred that one wouldn't consider that seed type relevant.)

Compare the above with this version that uses a one-dimensional sequential color scale:

The white color still stands out more than necessary. Fix this using a gray color.

What else is grabbing your attention when it shouldn't? It's those gridlines. Push them into the background using white-out.

Dotmaps, and by extension, bubble maps are popular options for spatial data; but the scale of these maps can be deceiving. Here is an example of a poorly-scaled dot map:

The U.S. was primarily an agrarian economy in 1997, if you believe your eyes.

Here is a poorly-scaled bubble map:

New Yorkers have all become Citibikers, if you believe what you see.

Last week, I saw a nice dot map embedded inside this New York Times Graphics feature on the destruction of the Syrian city of Raqqa.

Before I conclude that the destruction was broadly felt, I'd like to check the scale on the map to make sure it doesn't have the problem seen above. What is helpful here is the scale provided on the map itself.

That line segment representing a quarter mile fits about 15 dots side by side. Then, I found out that a Manhattan avenue (longer) block is roughly a quarter mile. That means the map places about 15 buildings to an avenue block. In my experience, that sounds about right: I'd imagine 15-20 buildings per block.

So I'm convinced that the designer chose an appropriate scale to display the data. It is actually true that the entire city of Raqqa was pretty much annihilated by U.S. bombs.

This plot is available in two versions, one for gender and one for race. The key question being asked is whether the leadership in the newsroom is more or less diverse than the rest of the staff.

The story appears to be a happy one: in many newsrooms, the leadership roughly reflects the staff in terms of gender distribution (even though both parts of the whole compare disfavorably to the gender ratio in the neighborhoods, as we saw in the previous post.)

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Unfortunately, there are a few execution problems with this scatter plot.

First, take a look at the vertical axis labels on the right side. The labels inform the leadership axis. The mid-point showing 50-50 (parity) is emphasized with the gray band. Around the mid-point, the labels seem out of place. Typically, when the chart contains gridlines, we expect the labels to sit right around each gridline, either on top or just below the line. Here the labels occupy the middle of the space between successive gridlines. On closer inspection, the labels are correctly affixed, and the gridlines drawn where they are supposed to be. The designer chose to show irregularly spaced labels: from the midpoint, it's a 15% jump on either side, then a 10% jump.

I find this decision confounding. It also seems as if two people have worked on these labels, as there exists two patterns: the first is "X% Leaders are Women", and second is "Y% Female." (Actually, the top and bottom labels are also inconsistent, one using "women" and the other "female".)

The horizontal axis? They left out the labels. Without labels, it is not possible to interpret the chart. Inspecting several conveniently placed data points, I figured that the labels on the six vertical gridlines should be 25%, 35%, ..., 65%, 75%, in essence the same scale as the vertical axis.

Here is the same chart with improved axis labels:

Re-labeling serves up a new issue. The key reference line on this chart isn't the horizontal parity line: it is the 45-degree line, showing that the leadership has the same proprotion of females as the rest of the staff. In the following plot (right side), I added in the 45-degree line. Note that it is positioned awkwardly on top of the grid system. The culprit is the incompatible gridlines.

The solution, as shown below, is to shift the vertical gridlines by 5% so that the 45-degree line bisects every grid cell it touches.

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Now that we dealt with the purely visual issues, let me get to a statistical issue that's been troubling me. It's about that yellow line. It's supposed to be a regression line that runs through the points.

Does it appear biased downwards to you? It just seems that there are too many dots above and not enough below. The distance of the furthest points above also appears to be larger than that of the distant points below.

How do we know the line is not correct? Notice that the green 45-degree line goes through the point labeled "AVERAGE." That is the "average" newsroom with the average proportion of female staff and the average proportion of leadership staff. Interestingly, the average falls right on the 45-degree line.

In general, the average does not need to hit the 45-degree line. The average, however, does need to hit the regression line! (For a mathematical explanation, see here.)

Note the corresponding chart for racial diversity has it right. The yellow line does pass through the average point here:

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In practice, how do problems seep into dataviz projects? It's the fact that you don't get to the last chart via a clean, streamlined process but that you pass through a cycle of explore-retrench-synthesize, frequently bouncing ideas between several people, and it's challenging to keep consistency!

And let me repeat my original comment about this project - the key learning here is how they took a complex dataset with many variables, broke it down into multiple parts addressing specific problems, and applied the layering principle to make each part of the project digestible.

Today, I take a detailed look at one of the pieces that came out of an amazing collaboration between Alberto Cairo, and Google's News Lab. The work on diversity in U.S. newsrooms is published here. Alberto's introduction to this piece is here.

The project addresses two questions: (a) gender diversity (representation of women) in U.S. newsrooms and (b) racial diversity (representation of white vs. non-white) in U.S. newsrooms.

One of the key strengths of the project is how the complex structure of the underlying data is displayed. The design incorporates the layering principle everywhere to clarify that structure.

At the top level, the gender and race data are presented separately through the two tabs on the top left corner. Additionally, newsrooms are classified into three tiers: brand-names (illustrated with logos), "top" newsrooms, and the rest.

The brand-name newsrooms are shown with logos while the reader has to click on individual bubbles to see the other newsrooms. (Presumably, the size of the bubble is the size of each newsroom.)

The horizontal scale is the proportion of males (or females), with equality positioned in the middle. The higher the proportion of male staff, the deeper is the blue. The higher the proportion of female staff, the deeper is the red. The colors are coordinated between the bubbles and the horizontal axis, which is a nice touch.

I am not feeling this color choice. The key reference level on this chart is the 50/50 split (parity), which is given the pale gray. So the attention is drawn to the edges of the chart, to those newsrooms that are the most gender-biased. I'd rather highlight the middle, celebrating those organizations with the best gender balance.

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The red-blue color scheme unfortunately re-appeared in a subsequent chart, with a different encoding.

Now, blue means a move towards parity while red indicates a move away from parity between 2001 and 2017. Gray now denotes lack of change. The horizontal scale remains the same, which is why this can cause some confusion.

Despite the colors, I like the above chart. The arrows symbolize trends. The chart delivers an insight. On average, these newsrooms are roughly 60% male with negligible improvement over 16 years.

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Back to layering. The following chart shows that "top" newsrooms include more than just the brand-name ones.

The dot plot is undervalued for showing simple trends like this. This is a good example of this use case.

While I typically recommend showing balanced axis for bipolar scale, this chart may be an exception. Moving to the right side is progress but the target sits in the middle; the goal isn't to get the dots to the far right so much of the right panel is wasted space.